Abstract

The capabilities and limitations of rainbow refractometry, specifically the minimum measurable droplet size and the errors in the refractive index (temperature), have been studied. We evaluate what we believe is a new method of indirectly applying the Lorenz-Mie theory to rainbow refractometry. The results show that this new method reduces the errors and eliminates the biases that may occur if the Airy theory is used. A more precise method to filter the high-frequency oscillations associated with the measurement signals was developed. Finally, it was discovered that the errors associated with rainbow refractometry are such that a single droplet measurement is unreliable. A mean refractive index should be determined on the basis of multiple droplet measurements.

© 2002 Optical Society of America

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  1. W. D. Bachalo, “Spray diagnostics for the twenty-first century,” Atomization Sprays 10, 439–474 (2000).
  2. F. Durst, M. Zare, “Laser Doppler measurements in two-phase flow,” in Proceedings of the LDA Symposium (Hemisphere, Washington, D.C., 1975), pp. 403–429.
  3. W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).
    [CrossRef]
  4. A. M. Murray, L. A. Melton, “Fluorescence methods for determination of temperature in fuel sprays,” Appl. Opt. 24, 2783–2787 (1985).
    [CrossRef] [PubMed]
  5. M. Seaver, J. R. Peele, “Noncontact fluorescence thermometry of acoustically levitated water drops,” Appl. Opt. 29, 4956–4961 (1990).
    [CrossRef] [PubMed]
  6. M. S. Atakan, A. R. Jones, “Measurement of particle size and refractive index using crossed-beam laser anemometry,” J. Phys. D 15, 1–13 (1982).
    [CrossRef]
  7. P. Massoli, F. Beretta, A. D’Alessio, M. Lazzaro, “Temperature and size of single transparent droplets by light scattering in the forward and rainbow regions,” Appl. Opt. 32, 3295–3301 (1993).
    [CrossRef] [PubMed]
  8. N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
    [CrossRef]
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  12. S. V. Sankar, D. M. Robart, W. D. Bachalo, “An advanced rainbow signal processor for improved accuracy in droplet temperature measurements,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.
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    [CrossRef] [PubMed]
  14. S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Simultaneous measurements of droplet size, velocity, and temperature in a swirl-stabilized spray flame,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.
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    [CrossRef]
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  19. H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
    [CrossRef]
  20. H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).
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    [CrossRef]
  22. E. A. Hovenac, J. A. Lock, “Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” J. Opt. Soc. Am. A 9, 781–795 (1992).
    [CrossRef]

2000 (2)

W. D. Bachalo, “Spray diagnostics for the twenty-first century,” Atomization Sprays 10, 439–474 (2000).

G. Gouesbet, G. Grehan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

1999 (1)

H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

1996 (1)

1995 (2)

H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).

J. P. A. J. van Beeck, M. L. Riethmuller, “Nonintrusive measurements of temperature and size of single falling raindrops,” Appl. Opt. 34, 1633–1639 (1995).
[CrossRef] [PubMed]

1993 (1)

1992 (1)

1991 (1)

1990 (2)

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

M. Seaver, J. R. Peele, “Noncontact fluorescence thermometry of acoustically levitated water drops,” Appl. Opt. 29, 4956–4961 (1990).
[CrossRef] [PubMed]

1988 (1)

1985 (2)

I. Thormalen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

A. M. Murray, L. A. Melton, “Fluorescence methods for determination of temperature in fuel sprays,” Appl. Opt. 24, 2783–2787 (1985).
[CrossRef] [PubMed]

1984 (1)

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

1982 (1)

M. S. Atakan, A. R. Jones, “Measurement of particle size and refractive index using crossed-beam laser anemometry,” J. Phys. D 15, 1–13 (1982).
[CrossRef]

Albrecht, H. E.

H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).

Anders, K.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Atakan, M. S.

M. S. Atakan, A. R. Jones, “Measurement of particle size and refractive index using crossed-beam laser anemometry,” J. Phys. D 15, 1–13 (1982).
[CrossRef]

Bachalo, W. D.

W. D. Bachalo, “Spray diagnostics for the twenty-first century,” Atomization Sprays 10, 439–474 (2000).

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fridrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

S. V. Sankar, D. M. Robart, W. D. Bachalo, “An advanced rainbow signal processor for improved accuracy in droplet temperature measurements,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Simultaneous measurements of droplet size, velocity, and temperature in a swirl-stabilized spray flame,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Bech, H.

H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).

Beretta, F.

Borys, M.

H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

Buermann, D. H.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Simultaneous measurements of droplet size, velocity, and temperature in a swirl-stabilized spray flame,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fridrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

D’Alessio, A.

Damaschke, N.

H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).

Durst, F.

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flow,” in Proceedings of the LDA Symposium (Hemisphere, Washington, D.C., 1975), pp. 403–429.

Feleke, M.

H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).

Fridrich, M. J.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fridrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

Frohn, A.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Gouesbet, G.

G. Gouesbet, G. Grehan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

Grehan, G.

G. Gouesbet, G. Grehan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

Grigull, U.

I. Thormalen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Houser, M. J.

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

Hovenac, E. A.

Ibrahim, K. M.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fridrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

Jones, A. R.

M. S. Atakan, A. R. Jones, “Measurement of particle size and refractive index using crossed-beam laser anemometry,” J. Phys. D 15, 1–13 (1982).
[CrossRef]

Lazzaro, M.

Lock, J. A.

Massoli, P.

Melton, L. A.

Murray, A. M.

Peele, J. R.

Riethmuller, M. L.

Robart, D. M.

S. V. Sankar, D. M. Robart, W. D. Bachalo, “An advanced rainbow signal processor for improved accuracy in droplet temperature measurements,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

Roth, N.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Sankar, S. V.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Simultaneous measurements of droplet size, velocity, and temperature in a swirl-stabilized spray flame,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fridrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

S. V. Sankar, D. M. Robart, W. D. Bachalo, “An advanced rainbow signal processor for improved accuracy in droplet temperature measurements,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

Schmidt, E.

E. Schmidt, Properties of Water and Steam in SI-Units (Springer, München, Germany, 1969).

Seaver, M.

Straub, J.

I. Thormalen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Thormalen, I.

I. Thormalen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Tropea, C.

H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

van Beeck, J. P. A. J.

van de Hulst, H. C.

Wang, R. T.

Zare, M.

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flow,” in Proceedings of the LDA Symposium (Hemisphere, Washington, D.C., 1975), pp. 403–429.

Appl. Opt. (6)

Atomization Sprays (2)

G. Gouesbet, G. Grehan, “Generalized Lorenz-Mie theories, from past to future,” Atomization Sprays 10, 277–333 (2000).

W. D. Bachalo, “Spray diagnostics for the twenty-first century,” Atomization Sprays 10, 439–474 (2000).

J. Laser Appl. (1)

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. Chem. Ref. Data (1)

I. Thormalen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

J. Phys. D (1)

M. S. Atakan, A. R. Jones, “Measurement of particle size and refractive index using crossed-beam laser anemometry,” J. Phys. D 15, 1–13 (1982).
[CrossRef]

Meas. Sci. Technol. (1)

H. E. Albrecht, M. Borys, N. Damaschke, C. Tropea, “The imaging properties of scattering particles in laser beams,” Meas. Sci. Technol. 10, 564–574 (1999).
[CrossRef]

Opt. Eng. (1)

W. D. Bachalo, M. J. Houser, “Phase/Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).
[CrossRef]

Optik (1)

H. E. Albrecht, H. Bech, N. Damaschke, M. Feleke, “Berechnung der Streuintensitaet eines beliebig im Laserstrahl positionierten Teilchens mit Hilfe der zweidimensionalen Fouriertransformation,” Optik 100, 118–124 (1995).

Other (6)

E. Schmidt, Properties of Water and Steam in SI-Units (Springer, München, Germany, 1969).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Simultaneous measurements of droplet size, velocity, and temperature in a swirl-stabilized spray flame,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flow,” in Proceedings of the LDA Symposium (Hemisphere, Washington, D.C., 1975), pp. 403–429.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fridrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

S. V. Sankar, D. M. Robart, W. D. Bachalo, “An advanced rainbow signal processor for improved accuracy in droplet temperature measurements,” presented at the Eighth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996.

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Figures (11)

Fig. 1
Fig. 1

Refractive index and temperature curves for pure water.

Fig. 2
Fig. 2

First three orders of light scattering from a sphere.

Fig. 3
Fig. 3

Simulated signals determined with the FLMT for a 100- and 50-µm droplet.

Fig. 4
Fig. 4

Power spectrums derived from simulated signals (50-µm droplet with and without the high-frequency oscillations on the supernumerary arcs).

Fig. 5
Fig. 5

Filter cutoff frequencies as a function of droplet diameter.

Fig. 6
Fig. 6

Error in refractive index associated with the Airy theory.

Fig. 7
Fig. 7

Error in diameter associated with the Airy theory.

Fig. 8
Fig. 8

Supernumerary arcs for small droplets as determined by the FLMT.

Fig. 9
Fig. 9

Angle of the first intensity peak associated with the supernumerary arcs as a function of diameter.

Fig. 10
Fig. 10

Error in refractive index associated with the application of the Airy theory and the PDI and rainbow refractometry diameter comparison validation methodology (criterion, ±5% of diameter).

Fig. 11
Fig. 11

Error in refractive index associated with the application of the Lorenz-Mie theory and the PDI and rainbow refractometry diameter comparison validation methodology (criterion, ±5% of diameter).

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